On the space of quantum fields in massive two-dimensional theories

For a large class of integrable quantum field theories we show that the S-matrix determines a space of fields which decomposes into subspaces labeled, besides the charge and spin indices, by an integer k. For scalar fields k is non-negative and is naturally identified as an off-critical extension of the conformal level. To each particle we associate an operator acting in the space of fields whose eigenvectors are primary (k = 0) fields of the massive theory. We discuss how the existing results for models as different as Z(n), sine-Gordon or Ising with magnetic field fit into this classification. (C) 2008 Elsevier B.V. All rights reserved.